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Thread: Prove that matrix is invertible

  1. #1
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    Prove that matrix is invertible

    A is a matrix, I is identity matrix and there exists such n that A^n=4A^3+3A^2+2A+I and i have to prove that A is invertible. so i think we have to find such B that AB=I, then A(A^{n-1}-4A^2-3A-2)=I but obviously "-2" is bad here.. AI=A so maybe A(A^{n-1}-4A^2-3A-2)=AI(A^{n-1}-4A^2-3A-2)=A(A^{n-1}-4A^2-3A-2I)=I makes proof right?
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  2. #2
    MHF Contributor

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    Yes, that is correct. Well done!

    (Although it would have made more sense to write 2A as (2I)A immediately.)
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